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People often say you should go for number diversity in your initial settlements. Obviously having higher-probability numbers is good, but is 6-9-4 and 8-5-10 really better than 8-5-10 and 8-5-10?

I'd say having repeated numbers is better, as it allows you to get your resources in a clump, allowing quick and surprising expansion. Often I've won a game this way from 8VPs, whilst others are on 9VPs and no-one is trading with them.

Am I wrong?

Does playing cities & knights make a difference to your opinion, where the Green bonus of a free resource makes my strategy even stronger?

6 Answers
6

Alex P's answer touches upon an interesting philosophical angle to this question. Suppose there are two strategies of game play in a four player game. Strategy A will reliably give you "good performance" (whatever that means for the current game - say 100 points) if carried out well; strategy B, if carried out well, gives you "bad performance" in 60% of your games (say 60 points) and "exceptionally good performance" 40% of the games (say 110 points).

In this (fictional) game, strategy A gives you better performance on average, but it may give you a lower probability of ending up in first place: in an environment where your three fellow players also play A, the game will be a toss up and strategy A will win you 25% of games, all other factors being equal, whereas strategy B will win you 40% of games. If your three fellow players play B, then strategy A will win only if all three of them have bad luck - less than 22% probability - and strategy B will turn it into a toss up again, so 25% wins. In both cases, strategy B will give you a higher probability of ending up in first place than strategy A.

Thus we see that even a relatively small chance of a relatively small improvement of your score over the alternative strategy may be worth a large risk of a really bad score - if all you care about is ending up first. However, you may prefer doing relatively well compared to your peers for certain, to having a slightly higher chance of winning overall but also a higher chance of ending up dead last. In that case, strategy A is better.

How does this apply to your question? Even if we leave the social aspects of the game aside (where players are more likely to impede further success of already successful players), going for clumped-up bunches of resources has some of the properties of strategy B: if you can ensure a steady trickle of resources, you will do well, but if you gamble the same number of settlements on a few numbers and they happen to come up more often, you will do even better - at the risk of losing badly if the dice don't go your way. Thus my answer is: all else being equal, spread the numbers if your objective is to do relatively well; concentrate the numbers if your objective is to have the highest chance of winning, and you're willing to accept a high risk of ending up last. (The key phrase in that sentence is "all else being equal", of course - in practice this consideration should be only one of many arguments when weighing different courses of action against one another.)

Number diversity is only part of the initial placing assessment where you also need to consider how you are going to win the game. Are you going for a brick / wood strategy or a wheat / ore strategy. The resources on the common numbers need to be complimentary resources and back your overall strategy or else there is little benefit in having common numbers (in this case having common numbers is probably a disadvantage). The best complimentary resources in my opinion are ore and wheat followed by wood and brick. An example of very weak complimentary resources is brick and ore or brick and sheep. Your example is a little extreme with every number being doubled up and I would prefer a constant stream of resources than periods of feast then famine. A constant stream of resources is important as in the beginning part of the game resource production grows exponentially tailing off in the later part of the game and it is important to not get behind the curve.

In conclusion I would value a common number on wheat and ore on a good number (5s, 6s, 8s or 9s) highly and with the right dice it could win the game easily. I once saw a situation where a player had engineered a position where rolling a 10 got the player 3 ore and 2 wheat. Two tens rolled very close together and the game effectively ended. However, good number coverage on complimentary resources is generally preferable. In general I think complimentary resources are the key element to initial placement which seems to get overlooked by a lot of players.

I think the effect of the aqueduct in cities and knights on my overall thinking would not make a considerable difference. The effect of the aqueduct would make me consider more whether to go a brick/wood strategy or a wheat/ore strategy rather than number placement.

On an abstract level, numbers diversity is preferable because it guarantees consistency, which enables more strategic play: if you've got a reliable trickle of resources coming it, it's easier to plan your development (Do I have the resource supply to go for a dev card strategy? Can I successfully race this other player to claim the port we both want, or is it not worth trying? If I build a city right now, am I going to be able to expand outward fast enough to avoid getting hemmed in?). Some players thrive on improvisation and surprise, though, and I can see them doing just as well with feast-or-famine placement. That means voluntarily becoming the underdog, in a sense -- but it's a totally practical move if you don't think you can beat the other players (either because of a skills gap or because their initial setup is stronger than any you could claim). If the most likely result of slow-and-steady play is that you'll just get more and more behind, you might as well gamble on an unbalanced setup!

Also, just mechanically speaking, Settlers has mechanics that specifically hose holding lots of resource cards at once (7s, Monopoly), so getting your resources all in one go puts you at risk for disruption.

I think the deciding factor is trading. Whichever approach you adopt, trades with other players do a lot to smooth out your early development. Some tables tend to clamp down and try to starve you out when they see that your development is likely to gradually outpace their own; others tend to be intimidated by big plays rather than overall board position. If the strategy you adopt costs you a lot of trading opportunities, it's probably going to be inferior in practice.

My overall intuition is that a good numbers spread is a generally better choice, but not as important as the right resource mixture or access to "good" numbers.

The simplest answer is NO. Here is how I would rank various features of your initial placement:

Quantity of resources (number of dots).

Availability of Brick and Lumber.

Availability of nearby ports.

Diversity of resources.

Room to expand.

Number diversity.

And like others have said, there is a certain upside in being focused on particular numbers. But however you feel about that, it should rarely decided where you place, given all of the more important factors for placement.

Number diversity is important - the best play is always with diverse numbers - but isn't the sole factor in winning. Diverse numbers gives you mimimum down-time, and maximizes income.

Diverse resources on those numbers are essential, as well, most of the time.

Use of 2:1 ports can mitigate concentrated resources, especially wheat if one as the wheat 2:1 and a concentration of wheat on good numbers. With the "standard" numbers layout for beginning games it's less important, but with the optional randomized number placement, and random tile placement, some spectacular ugliness can occur...

I once won as I had 5,6,8 on three adjacent wheat, and 6,8,9 on a wood, wheat and a brick. I was able to get to a wheat port in a couple turns, too. I was able to (due to some luck) build a city on turn 2 on the wheat. Turn 5 I had a wheat port... game was over by turn 20, and I'd won hands down... because I had a wheat port, and multiple cities on that wheat (which said, 2 of the tiles were map-edge).

You're probably familiar with the little red dots below the number values. Numbers 2 and 12 have one dot, while numbers 6 and 8 have five dots. The number of dots represents the odds that a number is rolled when rolling two dice, on average.

It's true that if you roll the dice thousands of times you will get more sevens than sixes. The problem is that a single game of Settlers is too short for the dice roll distribution to normalize. Within a 50 turn game, you can regularly get more 4s than 5s. You can get less 8s than 3s.

To counterbalance for these skewed odds, if you are presented with the choice of 5-6-6 or 5-6-8, the latter should be an easy choice because you spread the risk you're taking across your available numbers. You can only get screwed over for the numbers you don't have.